Lecture 2-B Practical Welltest Analysis

7/30/2019 Lecture 2-B Practical Welltest Analysis

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Practical WelltestAnalysis

Advanced Reservoir Engineering

Hassan Bahrami

2013


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Pressure vs Time in Transient Tests

Wellbore effect

Reservoir response

Boundary effect

Pressure

Time

PiPressure propagation, radial into formation

Boundary effect


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Wellbore storage analysis

Taking Logarithm of the equation:

General form of equation for WBS effect:

For pressure data related to

wellbore storage region:

Plot ofP vs. time in a Log-log

plot, results in a unit slope line

Plot of P: dp/d[ln(t)] vs.

time in a Log-log plot, results in

a unit slope line

tP c

c)(][L)1(P)Log( Logtog

c)(][L1t))]P)/d(ln(Log[d( Logtog And by taking the derivatives :

Log(dt)

P

P

Log(dP)

+1

slope


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Pressure Draw-Down Test Analysis

Time

Flow rate

Pressure


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Pressure Derivative Method / Drawdown Test

P = m (log[t]) + b

m3.2t)(lnd

P)(d

]3.2log[][log0]t)(lnd

P)(d[ mtLog

P

P

))tln(-)tP1)/(ln(-(P2:P' 12

RF

P

&Pr

t


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Permeability and Skin from Pressure

derivative

mIARF

)log(*)*3.2(1 RFRFhr tmPP

hm

BQk o

*)*3.2(

***6.162

]23.3)log()*3.2(

[*1513.12

1

wt

hr

rc

k

m

PS

P

&

Pr

t


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Pressure Build-Up Analysis

Pwf Pws

t=0

Pi

t=tp


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Pressure Derivative Method / Build-Up Test

P = m (log[ tp+t / t]) + b

mtp

3.2

)t

t

(lnd

P)(d

]3.2log[]t[log0]

t])t)/((ln[d

P)(d[ m

t

Log

p

t])t)/((ln[d

P)(d'

ptP


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hm

BQk o*)*3.2(

6.162

]23.3)log()1

log(*3.2

[*1513.12

1

wtp

phr

rc

k

t

t

m

PS

Permeability and Skin from Pressure

derivative

m

))1(

log(*)*3.2(1pRF

RFp

RFhrtt

ttmPP

P

&

Pr

t


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Well Models


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Well Models

Hydraulic (Vertical) Fracture

Infinite conductivity

Finite (low) conductivity

Partial completed/perforated

Horizontal well


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Infinite-Conductivity or Uniform Flux

Vertical (Hydraulic) Fracture


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Infinite-Conductivity or Uniform Flux Vertical (Hydraulic)

Fracture

+1/2


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Example of Linear Flow Regime Analysis


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Finite-Conductivity Vertical

(Hydraulic) Fracture

+1/4

+1/2


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Example of Finite Conductivity Response


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Partial Completion (Limited Entry)


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Example of Spherical Flow Regime Analysis


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Limited Entry Response

-1/2

KrKs


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Horizontal wells


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Horizontal wells

0 slope +1/2 slope 0 slope


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Multi-lateral wells


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Question: Flow regimes in Slanted wells? Plot a typical

P and P curves vs time for the following case.


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Reservoir Models


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Homogeneous Reservoirs


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Composite Systems


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Gas-Condensate Reservoirs


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Layered Reservoirs (Dual Permeability Model)

Welltest analysis using IARF line provides average permeability

and skin for multi-layered systems


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Welltest in 2-Layered Reservoirs


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Multi-Layered Reservoirs

Welltest Analysis


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Naturally fractured Reservoirs

Dual porosity

Dual permeabilityModel

ebulk volumMatrix

volumedMatrix voim

ebulk volumTotal

volumevoidFracturef


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Dual Porosity - Dual Permeability Reservoirs

Naturally Fractured

Reservoirs

(NFRs) Fracture radial

flow

Total system

radial flow

Km, PHIm Kf, PHIf


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Fracture Parameters

2

w

f

m rK

K

mmff

ff

CC

C

..

.

)/1/1/1(4222

ZYXaaa

K Permeability

C Compressibility

rw Wellbore radius

Porosity

a Fracture spacing (block size)

Shape factor

Interporosity flow coefficient

Fracture storativity

f fracture

m matrix

Image Logs

Petrophysical Logs

a

bImage Logs may provide

fracture aperture (b) and

fracture spacing (a)


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NFRs welltest analysis

SPE 104056

2

wm

f rK

K


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Question: Predict flow regimes for the following case, and

make plot of P&P vs time on Log-Log plot

water injection

Perf

Heavy Oil (API 15)Water

(Salinity 20000

PPM)


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Boundary Models


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Type of Boundaries

Fault ( Sealing fault Leaky fault )

Closed Systems (No flow Boundary)

Constant Pressure Boundary

(Aquifer - Gas Cap)


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Effect of Fault

Fault:

In early time: DP = m1 * log(Dt) + b

In late time: DP = m2 * log(Dt) + b

Where : m2 = 2 * m1

Closed Systems : DP = m * Dt + b

Result:

Log [ dP/d[log(Dt)] ] vs Log (Dt) Slope: +1


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Effect of Fault


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Leaky Fault


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Closed System: No flow boundary


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Constant

Pressure

Boundary

Aquifer

Gas cap


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Question: Predict flow regimes

Well

Boundary

Q ti


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Question:

Provide your interpretation on the pressure build-up data

given below.-Well model?

-Reservoir model?

-Boundary model?


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Welltest Analysis Using ECRIN

Hassan Bahrami


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Production time

Production rate

60 100024 0

60 hrs production with 1000 STBD oil rate,

followed by 24 hrs build-up


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60

1000


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Flow Regimes Prediction

using

Ecrin Numerical


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Add girds, then double click on well location


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Results


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Results1 2

How to remove grids:


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How to remove grids:

Right click:

Example of different time steps


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Example of different time steps

5 hrs 20 hrs

Linear & Elliptical flow Gradually changing toradial flow


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Thank you

Lecture 2-B Practical Welltest Analysis

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